Question

Case Study Chapter 5 Math Applications Direetions: Based on the data provided below, answer completely the following questions. You must show ALL work in order to receive full credit. Your submission can be a handwritten write-up that is scanned and submitted as a PDF or JPG file OR a typed write-up submitted as a DOC file. It must be submitted through the original case study link. The case study is worth 60 points. The following figure is the floor plan of an office complex он OH-Outside hallway W- Waiting room R-Reception area P - President's office L- Large meeting room H- Hallway Si - Storage room 1 S2 -Storage room 2 Ci-Conference room1 C: -Conference room2 So - Secretary's office CR-Computer room A - Accounting V - Vice president's office Ci 50 Ca CR 1. In a graph modeling this situation, each vertex would represent a location (type of room) and each edge would represent a door. a. How many vertices would be in the graph? (3 points) b. How many edges would be in the graph? (3 points) 2. Draw the graph that models this situation. Make sure your amount of vertices and edges correspond to your answer to question 1 and to the actual amount of locations and doors shown on the map. (16 points) 3. In the graph, are there any edges that act as bridges? Explain your answer. (4 points) 4. What are the degrees of each vertex on the graph? (14 points) 5. Is it possible to start and end in the outside hallway (OH) of the complex and walk through each door of the complex exactly once? Explain why or why not by using appropriate theorems and referring to your graph of the complex. (10 points) 6. Is it possible to start and end in different locations and walk through every door once in the complex? Explain why or why not by using appropriate theorems and referring to your graph of the complex. If it is possible, indicate what locations would be the starting and ending points. (10 points)

Answer 1

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